The COVID-19 pandemic led several countries to resort to social distancing, the only known way to slow down the spread of the virus and keep the health system under control. Here we use an individual based model (IBM) to study how the duration, start date and intensity of quarantine affect the height and position of the peak of the infection curve. We show that stochastic effects, inherent to the model dynamics, lead to variable outcomes for the same set of parameters, making it crucial to compute the probability of each result. To simplify the analysis we divide the outcomes in only two categories, that we call best and worst scenarios. Although long and intense quarantine is the best way to end the epidemic, it is very hard to implement in practice. Here we show that relatively short and intense quarantine periods can also be very effective in flattening the infection curve and even killing the virus, but the likelihood of such outcomes are low. Long quarantines of relatively low intensity, on the other hand, can delay the infection peak and reduce its size considerably with more than 50% probability, being a more effective policy than complete lockdown for short periods.Fractional calculus provides a promising tool for modeling fractional dynamics in computational biology, and this study tests the applicability of fractional-derivative equations (FDEs) for modeling the dynamics and mitigation scenarios of the novel coronavirus for the first time. The coronavirus disease 2019 (COVID-19) pandemic radically impacts our lives, while the evolution dynamics of COVID-19 remain obscure. A time-dependent Susceptible, Exposed, Infectious, and Recovered (SEIR) model was proposed and applied to fit and then predict the time series of COVID-19 evolution observed over the last three months (up to 3/22/2020) in China. The model results revealed that 1) the transmission, infection and recovery dynamics follow the integral-order SEIR model with significant spatiotemporal variations in the recovery rate, likely due to the continuous improvement of screening techniques and public hospital systems, as well as full city lockdowns in China, and 2) the evolution of number of deaths follows the timfatality and human activities.The Coronavirus Disease 2019 (COVID-19) surges worldwide. However, massive imported patients especially into Heilongjiang Province in China recently have been an alert for local COVID-19 outbreak. We collected data from January 23 to March 25 from Heilongjiang province and trained an ordinary differential equation model to fit the epidemic data. We extended the simulation using this trained model to characterize the effect of an imported 'escaper'. We showed that an imported 'escaper' was responsible for the newly confirmed COVID-19 infections from Apr 9 to Apr 19 in Heilongjiang province. Stochastic simulations further showed that significantly increased local contacts among imported 'escaper', its epidemiologically associated cases and susceptible populations greatly contributed to the local outbreak of COVID-19. Meanwhile, we further found that the reported number of asymptomatic patients was markedly lower than model predictions implying a large asymptomatic pool which was not identified. We further forecasted the effect of implementing strong interventions immediately to impede COVID-19 outbreak for Heilongjiang province. Implementation of stronger interventions to lower mutual contacts could accelerate the complete recovery from coronavirus infections in Heilongjiang province. Collectively, our model has characterized the epidemic of COVID-19 in Heilongjiang province and implied that strongly controlled measured should be taken for infected and asymptomatic patients to minimize total infections.Since the new coronavirus (COVID-19) outbreak spread from China to other countries, it has been a curiosity for how and how long the number of cases will increase. This study aims to forecast the number of confirmed cases of COVID-19 in Italy, the United Kingdom (UK) and the United States of America (USA). In this study, grey model (GM(1,1)), nonlinear grey Bernoulli model (NGBM(1,1)) and fractional nonlinear grey Bernoulli model (FANGBM(1,1)) are compared for the prediction. Therefore, grey prediction models, especially the fractional accumulated grey model, are used for the first time in this topic and it is believed that this study fills the gap in the literature. This model is applied to predict the data for the period 19/03-22/04/2020 (35 days) and forecast the data for the period 23/04-22/05/2020. The number of cases of COVID-19 in these countries are handled cumulatively. The prediction performance of the models is measured by the calculation of root mean square error (RMSE), mean absolute percentage error (MAPE) and R2 values. It is obtained that FANGBM(1,1) gives the highest prediction performance with having the lowest RMSE and MAPE values and the highest R2 values for these countries. Results show that the cumulative number of cases for Italy, UK and USA is forecasted to be about 233000, 189000 and 1160000, respectively, on May 22, 2020 which corresponds to the average daily rate is 0.80%, 1.19% and 1.13%, respectively, from 22/04/2020 to 22/05/2020. The FANGBM(1,1) presents that the cumulative number of cases of COVID-19 increases at a diminishing rate from 23/04/2020 to 22/05/2020 for these countries.COVID-19 is an emerging and rapidly evolving pandemic around the world, which causes severe acute respiratory syndrome and results in substantial morbidity and mortality. To examine the transmission dynamics of COVID-19, we investigate the spread of this pandemic using Malaysia as a case study and scrutinise its interactions with some exogenous factors such as limited medical resources and false detection problems. To do this, we employ a simple epidemiological model and analyse this system using modelling and dynamical systems techniques. https://www.selleckchem.com/products/trastuzumab-emtansine-t-dm1-.html We discover some contrasting findings with respect to the observations of basic reproduction number while it is observed that R0 seems to provide a good description of transmission dynamics in simple outbreak scenarios, this quantity might mislead the assessment on the severity of pandemic when certain complexities such as limited medical resources and false detection problems are incorporated into the model. In particular, we observe the possibility of a COVID-19 outbreak through bistable behaviour, even when the basic reproduction number is less than unity.